Simple model of morphometric constraint on carbon burial in boreal lakes - Cael, B. B.; Seekell, David A. (Frontiers in Environmental Science, 2023)
We developed a geometric theory to explain the empirical relationship between carbon burial and lake shape in boreal lakes. The key feature of this model is an attenuation length-scale, analogous to models of marine organic carbon fluxes. This length-scale is the ratio of how fast carbon is displaced vertically versus how fast it is respired, and engenders a simple model with a single easily constrained free parameter. Lake depths are modeled based on fractal area-volume relationships that reflect the approximate scale invariance of Earth’s topography and on idealized lake geometries. Carbon burial is estimated by applying the attenuation length-scale to these depths. Using this model, we demonstrate the relationship between dynamic ratio – a metric of lake morphometry calculated by dividing the square root of surface area by the mean depth – and carbon burial. We use scaling relationships to predict how dynamic ratio, and by extension carbon burial, varies across the lake size spectrum. Our model also provides a basis for generalizing empirical studies to the biome scale. By applying our model to a boreal lake census, we estimate boreal lake carbon burial is 1.8±0.5gC/m2/yr or 1.1±0.3TgC/yr among all boreal lakes.